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2 years ago

X: ax squared = bx? can someone help me

Mathematics

1 answer:

SSSSS [86.1K]2 years ago

6 0

Step-by-step explanation:

ax² = bx

ax² − bx = 0

x (ax − b) = 0

x = 0 or b/a

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Which function has a vertex on the y-axis? f(x) = (x – 2)2 f(x) = x(x + 2) f(x) = (x – 2)(x + 2) f(x) = (x + 1)(x – 2)

strojnjashka [21]

we know that

If the vertex is on the y-axis, then the x-coordinate of the vertex is equal to zero

we are going to verify the vertex of each one of the functions to determine the solution

Remember that

The equation in vertex form of a vertical parabola is equal to

$y=a(x-h)^{2} +k$

where

(h,k) is the vertex

if $a>0$ -------> the parabola open upward (vertex is a minimum)

if $a$ -------> the parabola open downward (vertex is a maximun)

case A) $f(x)=(x-2)^{2}$

This is a vertical parabola open upward

the vertex is the point $(2,0)$

therefore

The function $f(x)=(x-2)^{2}$ does not have a vertex on the y-axis

case B) $f(x)=x(x+2)$

$f(x)=x(x+2)=x^{2}+2x$

convert to vertex form

Complete the square. Remember to balance the equation by adding the same constants to each side.

$f(x)+1=x^{2}+2x+1$

Rewrite as perfect squares

$f(x)+1=(x+1)^{2}$

$f(x)=(x+1)^{2}-1$

the vertex is the point $(-1,-1)$

therefore

The function $f(x)=x(x+2)$ does not have a vertex on the y-axis

case C) $f(x)=(x-2)(x+2)$

$f(x)=(x-2)(x+2)=x^{2}-2^{2}$

$f(x)=x^{2}-4$

the vertex is the point $(0,-4)$

The x-coordinate of the vertex is equal to zero

therefore

The function $f(x)=(x-2)(x+2)$ has a vertex on the y-axis

case D) $f(x)=(x+1)(x-2)$

$f(x)=(x+1)(x-2)\\ \\f(x)= x^{2}-2x+x-2 \\ \\f(x)= x^{2} -x-2$

convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)+2= x^{2} -x$

Complete the square. Remember to balance the equation by adding the same constants to each side.

$f(x)+2+0.25= x^{2} -x+0.25$

$f(x)+2.25= x^{2} -x+0.25$

Rewrite as perfect squares

$f(x)+2.25= (x-0.50)^{2}$

$f(x)=(x-0.50)^{2}-2.25$

the vertex is the point $(0.5,-2.25)$

therefore

The function $f(x)=(x+1)(x-2)$ does not have a vertex on the y-axis

the answer is

$f(x)=(x-2)(x+2)$

6 0

3 years ago

Read 2 more answers

Mark took a loan out for $25,690 to purchase a truck. At an interest rate of 5.2% compounded annually, how much total will he ha

Inga [223]

Answer:

I think the answer is 1335.88

Step-by-step explanation:

5.2% of 25,690 is 1335.88

3 0

3 years ago

Read 2 more answers

What is the value of 30-2(7+2)-1

Firdavs [7]

Answer: 11

Step-by-step explanation:

30 - 2(7+2)- 1 Distribute or solve parentheses

30 - 14 -4 - 1

30 - 19 = 11

6 0

3 years ago

Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.

lubasha [3.4K]

Answer:

The answer is option C.

Step-by-step explanation:

The arithmetic sequence is given by

$A(n) = - 6 + (n - 1)( \frac{1}{5} )$

where n is the number of terms

For the first term

n = 1

So we have

$A(1) = - 6 + (1 - 1)( \frac{1}{5} )$

$= - 6 + (0)( \frac{1}{5} )$

$= - 6$

For the fourth term

n = 4

$A(4) = - 6 + (4 - 1)( \frac{1}{5} )$

$= - 6 + (3)( \frac{1}{5} )$

$= - 5 \frac{2}{5}$

For the tenth term

n = 10

$A(10) = - 6 + (10 - 1)( \frac{1}{5} )$

$= - 6 + (9)( \frac{1}{5} )$

$= - 4 \frac{1}{5}$

Hope this helps you

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3 years ago

Simplify 2x^2-1+4x^2-5

alekssr [168]

Answer:

6x^2-6

Step-by-step explanation: algebra

8 0

3 years ago